diff --git a/src/main/java/com/fasterxml/jackson/databind/deser/std/JsonNodeDeserializer.java b/src/main/java/com/fasterxml/jackson/databind/deser/std/JsonNodeDeserializer.java
index be1ba31d69..7a7e6095c2 100644
--- a/src/main/java/com/fasterxml/jackson/databind/deser/std/JsonNodeDeserializer.java
+++ b/src/main/java/com/fasterxml/jackson/databind/deser/std/JsonNodeDeserializer.java
@@ -755,12 +755,11 @@ protected final JsonNode _fromFloat(JsonParser p, DeserializationContext ctxt,
             return _fromBigDecimal(ctxt, nodeFactory, p.getDecimalValue());
         }
         if (ctxt.isEnabled(DeserializationFeature.USE_BIG_DECIMAL_FOR_FLOATS)) {
-            // 20-May-2016, tatu: As per [databind#1028], need to be careful
-            //   (note: JDK 1.8 would have `Double.isFinite()`)
-            if (p.isNaN()) {
-                return nodeFactory.numberNode(p.getDoubleValue());
+            try {
+                return _fromBigDecimal(ctxt, nodeFactory, p.getDecimalValue());
+            } catch (NumberFormatException nfe) {
+                // fall through - BigDecimal does not support values like NaN
             }
-            return _fromBigDecimal(ctxt, nodeFactory, p.getDecimalValue());
         }
         if (nt == JsonParser.NumberType.FLOAT) {
             return nodeFactory.numberNode(p.getFloatValue());
diff --git a/src/test/java/com/fasterxml/jackson/databind/NumberNodes1770Test.java b/src/test/java/com/fasterxml/jackson/databind/NumberNodes1770Test.java
new file mode 100644
index 0000000000..96ccf27999
--- /dev/null
+++ b/src/test/java/com/fasterxml/jackson/databind/NumberNodes1770Test.java
@@ -0,0 +1,43 @@
+package com.fasterxml.jackson.databind;
+
+import com.fasterxml.jackson.core.JsonFactory;
+import com.fasterxml.jackson.core.json.JsonReadFeature;
+import com.fasterxml.jackson.databind.json.JsonMapper;
+
+import java.math.BigDecimal;
+
+/**
+ * Basic tests for {@link JsonNode} implementations that
+ * contain numeric values.
+ */
+public class NumberNodes1770Test extends BaseMapTest
+{
+    private final ObjectMapper MAPPER = newJsonMapper();
+
+    // For to [databind#1770] (broken due to fix for #1028): `JsonNodeDeserializer`
+    // would coerce ok but does `parser.isNaN()` check which ends up parsing
+    // as Double, gets `POSITIVE_INFINITY` and returns `true`: this results in
+    // `DoubleNode` being used even tho `BigDecimal` could fit the number.
+    public void testBigDecimalCoercion() throws Exception
+    {
+        final String value = "7976931348623157e309";
+        final JsonNode jsonNode = MAPPER.reader()
+            .with(DeserializationFeature.USE_BIG_DECIMAL_FOR_FLOATS)
+            .readTree(value);
+        assertTrue("Expected DecimalNode, got: "+jsonNode.getClass().getName()+": "+jsonNode, jsonNode.isBigDecimal());
+        assertEquals(new BigDecimal(value), jsonNode.decimalValue());
+    }
+
+    public void testBigDecimalCoercionInf() throws Exception
+    {
+        final String value = "+INF";
+        JsonFactory factory = JsonFactory.builder()
+                .enable(JsonReadFeature.ALLOW_NON_NUMERIC_NUMBERS)
+                .build();
+        final JsonNode jsonNode = new JsonMapper(factory).reader()
+                .with(DeserializationFeature.USE_BIG_DECIMAL_FOR_FLOATS)
+                .readTree(value);
+        assertTrue("Expected DoubleNode, got: "+jsonNode.getClass().getName()+": "+jsonNode, jsonNode.isDouble());
+        assertEquals(Double.POSITIVE_INFINITY, jsonNode.doubleValue());
+    }
+}
diff --git a/src/test/java/com/fasterxml/jackson/failing/NumberNodes1770Test.java b/src/test/java/com/fasterxml/jackson/failing/NumberNodes1770Test.java
deleted file mode 100644
index a2e18f0ff4..0000000000
--- a/src/test/java/com/fasterxml/jackson/failing/NumberNodes1770Test.java
+++ /dev/null
@@ -1,26 +0,0 @@
-package com.fasterxml.jackson.failing;
-
-import com.fasterxml.jackson.databind.*;
-
-/**
- * Basic tests for {@link JsonNode} implementations that
- * contain numeric values.
- */
-public class NumberNodes1770Test extends BaseMapTest
-{
-    private final ObjectMapper MAPPER = newJsonMapper();
-
-    // For to [databind#1770] (broken due to fix for #1028): `JsonNodeDeserializer`
-    // would coerce ok but does `parser.isNaN()` check which ends up parsing
-    // as Double, gets `POSITIVE_INFINITY` and returns `true`: this results in
-    // `DoubleNode` being used even tho `BigDecimal` could fit the number.
-    public void testBigDecimalCoercion() throws Exception
-    {
-        final JsonNode jsonNode = MAPPER.reader()
-            .with(DeserializationFeature.USE_BIG_DECIMAL_FOR_FLOATS)
-            .readTree("7976931348623157e309");
-        assertTrue("Expected DecimalNode, got: "+jsonNode.getClass().getName()+": "+jsonNode, jsonNode.isBigDecimal());
-        // the following fails with NumberFormatException, because jsonNode is a DoubleNode with a value of POSITIVE_INFINITY
-//        Assert.assertTrue(jsonNode.decimalValue().compareTo(new BigDecimal("7976931348623157e309")) == 0);
-    }
-}